Non-linear functional operator



March 9, 1965 3,173,024

R. PERETZ NON-LINEAR FUNCTIONAL OPERATOR Filed July 14, 1961 2 Sheets-Sheet l Z E NEK C A'THODE Summation Circuit INVENTOR RICHARD PERE TZ ATTORNEYS 2 Sheets-Sheet 2 Filed July '14. 1961 Amplifier INVENTOR ATTORNEYS d" ll-lull. 1 Q o F u n u n n u j d n n u u n u 2 u llll 2 m v a r my E 7 mm 0L 0 9 o 9 n r 0 r w w H .w EA t a W. Z: O1 HO 0L P0 01 W m m a m A 9 5 01 0 9 O 1% 2 Q I 9 Q n m u n H 8 m m m t--- m m T E r F r l a w J m f Q n m w n n v n n m m T 5 my. 5 hr HO 9 |l||||. |O 01 Fix r. P 1 F 9 F 9 z I II x J A J Q L n n u n n l 5 Ar K 2 M w T E z United States Patent 3,173,024 NON-LINEAR FUNQTIONAL OPERATOR Richard Peretz, Watermael-Boitsfort, Belgium, assignor to Ateliers de Constructions Electriques de Charleroi (ACEC), Brussels, Belgium, a joint-stock company of Belgium Filed July 14, 1961, Ser. No. 124,137 2 Claims. (Cl. 307-885) This invention relates to a new type of a circuit, called non-linear functional operator, delivering an output signal which is a dependent variable of the input voltage according to a nonlinear function. Such operators can be used in automatic regulation systems and in electronic analog computers.

A known principle of operation of such circuits consists of producing an output signal which varies as the input voltage according to a function which can be represented by a broken line constituting an approximation of the desired function. This principle has been disclosed in the book Electronic Analog Computers" by Korn, A. G. and Korn, T. M. pages 290 to 297 (McGraw- Hill, New York, 1956).

A general object of the present invention is to provide a non-linear functional operator which operates according to the above-mentioned principle, simple and ac curate, easy to use, sturdy and stable.

Another object of the invention is to provide a nonlinear functional operator comprising branches each constituted by Zener diodes connected in series at the junction points of which voltages appear which can be rep resented, as a function of the input voltage, by straight lines intersecting the horizontal axes in spaced points and comprising means for separately varying the slope of these linear voltages and for combining them so that the resulting voltage varies by approximation according to any desired non-linear function.

Further objects and advantages will readily become apparent upon reading the following specification taken in conjunction with the drawings in which:

FIG. 1 represents an element of a non-linear functional operator according to the invention;

FIG. 2 is a diagram showing the variation of output voltages of this element as a function of the input voltage;

FIG. 3 shows a circuit allowing the slope of these output voltages to be varied;

FIG. 4 is a schematic of a particular form of a nonlinear functional operator in which two elements as shown in FIG. 1 are used;

FIG. 5 is a schematic of another particular form of realization;

FIG. 6 shows a circuit for smoothing the angles of the variation of an output voltage represented by a broken line;

FIG. 7 shows a still further form of realization of an operator.

Referring to FIG. 1, Zener diodes Z Z Z Z are connected in series with a silicon diode D An input voltage V, being applied to terminals V with a polarity corresponding to the conduction direction of diode D and assuming that the input voltage increases, there will appear at terminals V a voltage V; once the Zener voltage of Z has been reached. This voltage V will vary according to FIG. 2, increasing from zero until when V has reached the Zener voltage of the second diode Z a voltage V appears which also increases from zero, and so forth. Thus voltages V V V V appear successively as the input voltage increases and will vary according to FIG. 2.

A second group of Zener diodes Z' Z' Z are connected in series with a second silicon diode D' having a conduction direction opposite to that of D so that,

3,173fi24 Patented Mar. 9, 1965 when the polarity of the input voltage V, is inverted, output voltages V V' V appear successively at the junction points of the different Zener diodes Z Z 2' The variation of these voltages V V V and V' V' V appearing at the corresponding output terminals when the input voltage in creases is shown at FIG. 2.

The silicon diodes D and D; are necessary to prevent direct conduction by the Zener diodes.

It is evident that all these voltages are represented by straight lines having the same slope but spaced from one another. In order to make possible the variation of the slope of these voltages, they are applied each to a potentiometer as shown at FIG. 3. For example, the slope of the output voltage V can be changed by adjusting the potentiometer P connected to the junction point of two adjacent Zener diodes Z and Z The sum of the voltages taken across the different potentiometers similar to P will constitute a resultant output voltage which varies according to a non-linear function of the input voltage, approached by a broken straight line, the slope of which continuously increases.

To produce an output voltage varying according to an arbitrary function of the input voltage, the circuit shown at FIG. 4 may be employed. It comprises two elements similar to that of FIG. 1, fed by equal voltages but having opposite polarities.

The first element is constituted by the Zener diodes Z11, Z21, Z311; Z u, Z m, 21 and thfi SlllCOIl diodes D and D Potentiometers P P P P111; P' P P are connected between the ground and the common point of the silicon diodes D and D' and the respective common points of the different Zener diodes. Similarly, the second element comprises the Zener diodes Z Z Z Z Z Z' z, the silicon diodes D D and the potentiometers P02, P12, P22 P112; P32, F zz P g. The tlVO elements are fed respectively by input voltages V and V, which are equal but of opposite polarities. The voltages taken at the dilferent potentiometers of the two elements are applied to a summation circuit S which supplies an output voltage V equal to the sum of these voltages. It is obvious that, by suitably adjusting the difierent otentiometers, any desired shape can be obice . tained for the output voltage V A particular embodiment shown at FIG. 5 allows replacement of the two series of Zener diodes of FIG. '4, by a single one, in cases where the output voltage is required to vary with the input voltage according to functions which are symmetrical with respect to the vertical axis. This layout, which results in an economy of half the Zener diodes, is particularly interesting for use in operations of the type:

FIG. 6 shows the application of the principle of smoothing the angles of the broken line representing the function. This principle has been disclosed by the inventor in a communication at the International Analogy Computation Meeting, September 1955. It consists of superimposing on the voltage at the junction point of two adjacent portions of the broken line a voltage, preferably of triangular shape as a function of time, having a frequency notably higher than the maximum frequency of the voltages applied to the operator. In the case of a triangular voltage, the smoothing has a parabolic shape.

In FIG. 6, high frequency signals supplied by suitable sources such as G G and each adjustable by means of potentiometers R R are applied through condensers C C to the potentiometers P P which are connected to the common points of the Zener diodes Z Z Z Z through respective silicon diodes d (I' the conduction. direction of which corresponds to the direction of the current fioWing from the input terminals-through the Zener diodes into the slope-adjusting-potentiometers.

"Referring now to FIG. 7 Whichrepresents a-complete schematic of a non-linear functional operatoriaccording to the invention, two series of Zener diodes and silicon diodes, designated by the'same refereneesas-in'FIG. .4, are fed with equal voltages, but havingopposite polarities, respectively supplied by an input amplifier} and-an inverting amplifier 2. This-amplifier has a gainequal ml and it only invertsthepolarity of 'the' voltagesupplied-by the amplifier 1. The input voltage, atthe terminals? is applied togthe input ofthe amplifierl through aresistanee 4.

The junction-points-of the Zener diodes are connected through silicon diodes d p1 d d ,-d df and dlzfdzg (11, d' d' 'd the groups of which have alternate polarities,to'commutators, designated by thegeneral references-K K .K having movable contacts a a which can be operated manually orautomatically. The commutators are connected together so that: the voltage at any one of the junctoin points of the Zener diodes canqbe applied to any one of the leads b b b 'connected respectively-topotentiometers P ,-P P the voltages of which are applied, through resistances r r r to-the input of an output amplifier 5. -The potentiometers 'can' also be operated-manually or automatically. It can be readily understood that this amplifier receives the sum of in different voltages which can be chosen in any desired manner among the-different junction points'ofthe Zener diodes -to reproduce the desired non-linear function. The signal is amplified by the amplifier 5 and appears at its terminals 6. The gain ot-the amplifier;5 can be ad justed by means of a switch 7 and resistances such as 8, 9, 10.

T he smoothing of the angles of'the generated function is achieved as described above by applying high frequency voltages to the leads b b b through condensers C C C 'Thesevoltages are taken at potentiometers R R R fed by a suitable generator 11.

The generated function can be shifted horizontally by applying'to'the input terminal of the amplifier 1 a DC. voltage which can be adjusted positively ornegatively by means of a-potentiometer 1'2 fed by a suitableD.C. source 13. In the same manner,'the vertical shifting of the curve is achieved by applying to the input of the .amplifierS a DC. voltage; through a resistance 14, supplied by a source '15 and adjustable by means of a potentiometer 16.

Evidently-the invention is not exclusively limited to the embodimentsdescribed and,it'is possible to bring about several modifications in the shape, layout and constitution of some of the elements entering its realization without departing from the scope of the invention.

I claim: 1. A non-linear functional operator having input and output terminals, the output voltage of which is a nonlinear functionyof the input voltage, said function being graphically. representable by approximation by a broken line, comprising at least one branch constituted by aaplurality of Zener jdiodes connected in series, all in the same direction, said March being connected, at one end, to an input terminal, through a silicon diode poled to permit flowot current in the breakdown directionof'the' Zener diodes, aplurality of potentiometersconnected between the ground and respectively the inputterminal and each of the successive junction-points of thexZener diodes, and

a summation circuit to add the'voltages: taken at the difsilicon diode poled to permit fiow of current in the: breakdown direction of the Zener fdiodes,.the twowbranches having reverse directions of'lfiow with respect to =the common input: terminal, a plurality of potentiometers connected between the ground and respectively the input terminals and the successive function points of the. Zener diodes of both circuits, and a summation circuit-toadd the voltages taken at the different otentiometers, the output voltage of said: summation circuit being applied to the output terminal of the operator.

References Cited by. theExaminer UNITED STATES PATENTS 2,697,201 12/54 Harder 235-197 X 2,945,950 7/60 -Midkiff 307 -'8'8.5

OTHER REFERENCES Shaughnessy: The Zener DiodejPopular Electronics,

June 1961(pp. 76 to 82) (pp. 81v relied on).

Motorola Silicon ZeneriDiode 'Handbook,'2nd Edition, July 5,1961 (pp. relied on).

ARTHUR GAUSS, Primary Examiner.

JOHN W. HUCKERT, Examiner. 

1. A NON-LINEAR FUNCTIONAL OPERATOR HAVING INPUT AND OUTPUT TERMINALS, THE OUTPUT VOLTAGE OF WHICH IS A NONLINEAR FUNCTION OF THE INPUT VOLTAGE, SAID FUNCTION BEING GRAPHICALLY REPRESENTABLE BY APPROXIMATION BY A BROKEN LINE, COMPRISING AT LEAST ONE BRANCH CONSTITUTED BY A PLURALITY OF ZENER DIODES CONNECTED IN SERIES, ALL IN THE SAME DIRECTION, SAID BRANCH BEING CONNECTED, AT ONE END, TO AN INPUT TERMINAL, THROUGH A SILICON DIODE POLED TO PERMIT FLOW OF CURRENT IN THE BREAKDOWN DIRECTION OF THE ZENER DIODES, A PLURALITY OF POTENTIOMETERS CONNECTED BETWEEN THE GROUND AND RESPECTIVELY THE INPUT TERMINAL AND EACH OF THE SUCCESSIVE JUNCTION POINTS OF THE ZENER DIODES, AND A SUMMATION CIRCUIT TO ADD THE VOLTAGES TAKEN AT THE DIFFERENT POTENTIOMETERS THE OUTPUT VOLTAGE OF SAID SUMMATION CIRCUIT BEING APPLIED TO THE OUTPUT TERMINAL OF THE OPERATOR. 